A square loop of side 2 a, and carrying current I,


A square loop of side $2 a$, and carrying current $I$, is kept in $\mathrm{XZ}$ plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to the $z$-axis and passing through the point $(0, b, 0),(b>>a)$. The magnitude of the torque on the loop about $z$-axis is given by:

  1. (1) $\frac{\mu_{0} I^{2} a^{2}}{2 \pi b}$

  2. (2) $\frac{\mu_{0} I^{2} a^{3}}{2 \pi b^{2}}$

  3. (3) $\frac{2 \mu_{0} I^{2} a^{2}}{\pi b}$

  4. (4) $\frac{2 \mu_{0} I^{2} a^{3}}{\pi b^{2}}$

Correct Option: , 3


(3) Torque on the loop,

$\bar{\tau}=\bar{M} \times \bar{B}=M B \sin \theta=M B \sin 90^{\circ}$

Magnetic field, $B=\frac{\mu_{0} I}{2 \pi d}$

$\therefore \tau=I_{1}(2 a)^{2}\left(\frac{\mu_{0} I_{2}}{2 \pi d}\right) \sin 90^{\circ}$

$=\frac{2 \mu_{0} I_{1} I_{2}}{\pi d} \times a^{2}=\frac{2 \mu_{0} I^{2} a^{2}}{\pi d}$

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